You might be able to attach the vdi to a VirtualBox VM, and boot the VM from an Ubuntu live-cd .iso in the virtual cd drive. Ubuntu would most likely auto-mount the vdi, and you would be able to browse it via the file manager. If that works, you could conigure the VM to usea USB stickfor saving your files.
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Joe InternetOct 3 '11 at 5:30

@Joe Internet - I spent a greater part of Friday trying to do this with a Windows 7 boot image, but it would also freeze when I tried to attach the non booting vdi. I just tried attaching it to an old Ubuntu vdi I had from a while ago. Five minutes later, I had all my files back! Thanks for the tip!
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lagerdalekOct 3 '11 at 21:00